What is laplacetransform-9t^2+18t+7 ?

The answer to laplacetransform-9t^2+18t+7 is -(18)/(s^3)+(18)/(s^2)+7/s

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laplacetransform-9t^2+18t+7

laplace transform

- 9 t^{2} + 18 t + 7

- \frac{18}{s ^{3}} + \frac{18}{s ^{2}} + \frac{7}{s}

Solution steps

L {- 9 t^{2} + 18 t + 7}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= - 9 L {t^{2}} + 18 L {t} + L {7}

L {t^{2}} : \frac{2}{s ^{3}}

L {t} : \frac{1}{s ^{2}}

L {7} : \frac{7}{s}

= - 9 \cdot \frac{2}{s ^{3}} + 18 \cdot \frac{1}{s ^{2}} + \frac{7}{s}

Refine

- 9 \frac{2}{s ^{3}} + 18 \frac{1}{s ^{2}} + \frac{7}{s} : - \frac{18}{s ^{3}} + \frac{18}{s ^{2}} + \frac{7}{s}

= - \frac{18}{s ^{3}} + \frac{18}{s ^{2}} + \frac{7}{s}

y^{^{'}} + 2 y = 35 sin (t) + 35 cos (t)

\frac{d y}{d x}, x + y = 1

x = - 2 y^{2} - 4 y + 1, x = y^{2} + 8 y + 10

\frac{\partial}{\partial x} (e^{3 x yz - 8})

(- 2, - 10), (0, - 4)

What is laplacetransform-9t^2+18t+7 ?
The answer to laplacetransform-9t^2+18t+7 is -(18)/(s^3)+(18)/(s^2)+7/s